Abstraction and Modeling Transcription
[Title slide] In this video, we’ll discuss the concept of abstraction again. This time, we’re going
to focus on how we use abstraction in modeling and simulation.
[Slide 1] As we learned in the last video about abstraction, abstraction is simplification. Why
would we want to use abstraction when we’re modeling? Well, when you want to model a
problem, you’ll find that most real-world problems are just too complicated. In order to model
them, you must simplify them. Therefore, you must apply abstraction. This simplification means
that you must ignore some details or parts of the problem so that you can focus on what’s most
important to you at that time.As you interests change or your knowledge grows, the amount of
abstraction you need for your model may change too.
[Slide 2] Abstraction involves assumptions. Assumptions are things that you take to be true at
any given time. When you use assumptions before you do abstraction, it helps you in your
abstraction process, and also, after you’ve done abstraction, when you’re trying to take your
abstraction and make a model out of it.
Assumptions are what a modeler uses or assumes when moving from the real-world problem to
an actual model. Sometimes, that’s a simplification, and sometimes that’s a specification. What
do I mean by those two things? Sometimes, to just make an assumption so that it’s easier to do
the model. For instance, if you’re looking at a gigantic ecosystem, but you really are only
interested in rabbits, you might be able to ignore most other things besides rabbits. The
assumption in that case would be only rabbits are important to my model.
A specification might be that you know that each rabbit or each female rabbit would have six
baby rabbits every year. The birth rate for rabbits in your model would be specified to be six
rabbits per year. Assumptions need to be carefully considered because they affect the outcome
of the model. If the model is really important, then those assumptions should be validated.
[Slide 3] Here’s a picture of a pond ecosystem. There are a lot of things involved in a pond
ecosystem as you can see. We have everything from microorganisms and snails and slugs and
salamanders. We have insects, fish, beavers and snakes. There are a lot of animals involved in
the water itself. Then, there are animals that interact with the water and may affect the pond
ecosystem. For instance, raccoons don’t actually live in the water, but they may eat things that
are in the water so they affect the pond ecosystem.
Birds … some birds actually eat fish or other small animals inside the pond. We see people
fishing. We know that people interact with the ecosystem by fishing or by polluting. You can see
at the bottom of the lake here, there are some cans and bottles and plastic and other debris.
Another way that man interacts with the ecosystem is by farming or changing the land close to
the water. Farming can be particularly detrimental to a pond ecosystem because of run-off
from the farm, other run-off in terms of pesticides or manure or any other thing that you might
find in a farm.
Abstraction and Modeling Transcription
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Way in the distance, you see there’s a city. That city could actually affect the pond ecosystem if
any water that comes from the city or air pollution from the city reaches this pond
environment. It’s very, very complicated. Because it’s so complicated it is very difficult to
model. If you were interested, say, in how many bass there might be in this pond, and that’s
what you wanted to model because you like fish, then, you might not actually pay attention to
too many other parts of the ecosystem besides the bass and what the bass eats and what eats
the bass.
You might group the other things together in some way, to represent them if you find that they
are important. For instance, you might group all forms of pollution together and have that
affect the pond in some way. Your model might include bass, and maybe some small fish, if
that’s what bass eat or some insects, and perhaps fisherman because fisherman eat bass, and
perhaps otters. Here, we have an otter. That might eat the bass, I guess, small bass.
You might include those things in your model, and you might not include, say for instance,
snails, unless you know that bass eat snails which I don’t know. You might not include deer,
since deer might not interact in a way that affects the population of bass. Let’s move on to
another problem.
[Slide 4] Let’s say we want to apply abstraction to modeling a rabbit’s ecosystem, but we’re
mostly interested in the population of rabbits. Like with the pond, there are many things that
affect rabbits and rabbit populations. Living things affect the rabbit population and non-living
things affect rabbit populations.
The living things that could affect the rabbit population include the rabbit characteristics itself.
For instance, the birth rate, the death rate, the metabolism, how fast they digest their food,
and how much energy they use and infection. People might affect rabbit populations because
they might build homes where rabbits like to live, or they might hunt rabbits. Rabbits eat
plants, so the plants available to a rabbit are very important to the rabbit population.
Other animals are important to a rabbit population too. For instance, predators are critically
important to rabbit population, how many coyotes or foxes or rafters. Even microscopic things
could affect your rabbit population. For instance, some small microscopic infection could infect
the plants that the rabbit might eat.
The non-living things that could affect the rabbit population could include the water, water
quality, how much water there is, the soil, can the rabbit make a rabbit hole, to find a place to
live, will the plants grow in that soil, the weather, is it too wet or too dry for the rabbit
population to be optimal, any natural disasters and pollution. Those are a lot of things to
include in a model, so we would probably simplify that.
We would maybe include some rabbit characteristics, like the birth and death rate, and the fact
that rabbits expend energy just by living. We would have to include plants because rabbits eat
plants. We might create a simple model that includes just those things. Let’s go take a look.
Abstraction and Modeling Transcription
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[Slide 5] Here, we have the rabbits live model. Let’s look at the code. I’m only showing you just
the top part of the code here. We’re going to be looking primarily at the rabbits interacting with
their ecosystem. Here, we have rabbits move, rabbits eat, rabbits reproduce and rabbits die.
Rabbits move around using the wiggle motion, which you’re all familiar with. They gain energy
when they eat and they lose energy when they move around and when they reproduce. When
they have no energy they die.
Let’s take a look at the model. We have the net logo, two-dimensional plain with the green
squares of grass. We have the little rabbits distributed around the plain. If we hit the “rabbits
live”, we can see that the rabbits reproduce, and you get many more rabbits. They’re eating the
grass. They keep eating the grass until there’s no more grass left. Then, the rabbits start to die,
until eventually there are no more rabbits left.
This is, of course, not a very realistic model, since the rabbits have died off. We know in the real
world that we never seem to completely eliminate the rabbits from our environment so we
know that this is not a realistic model. That means we have to add more things to the model to
make it more realistic. Let’s go back to our list.
[Slide 6] This time, we’re going to add other animals to the model. Also, we’re going to have the
grass re-grow so the rabbits continuously have something to eat.
Let’s take a look at that. This time, we’ve added coyotes to our model with the rabbits and the
grass. The coyotes get energy from eating the rabbits. They lose energy by moving around and
by reproducing. We have two species, the rabbits and the coyotes that are eating to gain
energy, and are losing energy by reproducing and by moving around. When they lose all their
energy they die. Let’s see what happens.
The rabbit population increases, and then the coyote population increases. It goes back and
forth. We have the population at some sort of equilibrium a much more realistic situation.
[Slide 7] One thing that I did not show you in the modeling process was that I did have to
manipulate the birth rates and the energy value of the plants in order to get the model to
stabilize. There, you see, we can model a rabbit ecosystem and have a realistic outcome.
[Slide 8] In summary, abstraction is required for modeling. Different levels of interest will vary
the amount of abstraction that’s needed. Abstraction involves assumptions before, during and
after the abstraction process. Assumptions can affect the outcome of the model and should be
carefully considered and evaluated. Thank you.
Abstraction and Modeling Transcription
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